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Inverses of 2 × 2 block matrices [PDF]

Computers and Mathematics With Applications, 2002
In this paper, the authors give explicit inverse formulae for 2 × 2 block matrices with three different partitions. Then these results are applied to obtain inverses of block triangular matrices and various structured matrices such as Hamiltonian, per ...
Tzon-Tzer Lu
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A Block Generalization of Nekrasov Matrices

Journal of Mathematical Sciences, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Matrices Doubly Stochastic by Blocks

Canadian Journal of Mathematics, 1977
The present work stems from the following classical result, due to G. H. Hardy, J. E. Littlewood, G. Pólya [7], and R. Rado [10].THEOREM 1. Concerning a pair of n-tuples x, y ϵ Rn, the following four statementsare equivalent:(a) for every continuous, convex function f : R ...
Fischer, Pal, Holbrook, John A. R.
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On the Inverse of Block Tridiagonal Matrices with Applications to the Inverses of Band Matrices and Block Band Matrices

1989
In the present paper the authors make an attempt to give a uniform description of the main properties of tridiagonal, band, block tridiagonal and block band matrices and their inverses. Some basic concepts are recalled and also some new results are presented.
ROSZA P, BEVILACQUA, ROBERTO, FAVATI P, ROMANI, FRANCESCO   +3 more
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Symmetric Matrices with Alternating Blocks

1989
A statement in algebraic geometry over fields of arbitrary characteristic follows from the existence of matrices with integer entries of the type mentioned in the title. It is shown how these matrices can be built from a finite number of small matrices. It is reported how these small matrices, of which the largest is a 25 by 25 matrix, were found using
Hefez, Abramo, Thorup, Anders
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A POLYNOMIAL PRECONDITIONER FOR BLOCK TRIDIAGONAL MATRICES

Parallel Algorithms and Applications, 1994
ABSTRACT This paper is concerned with the solution of block tridiagonal linear systems by the preconditioned conjugate gradient (PCG) method. If we consider a block AGE splitting of the coefficient matrix, it is possible to derive an additive polynomial preconditioner and to give conditions for such preconditioner to be symmetric positive definite ...
GALLIGANI, Emanuele, V. RUGGIERO
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On the Index of Block Upper Triangular Matrices

SIAM Journal on Matrix Analysis and Applications, 1995
This paper gives a precise characterization of the size of the largest Jordan block for the eigenvalue zero (called the index) of \(M = [\begin{smallmatrix} A & X \\ 0 & B \end{smallmatrix}]\) where \(A\) and \(B\) are both singular in terms of statements about the powers of \(M\) and their diagonal block images and kernels, the height and depth of ...
Rafael Bru, Joan-Josep Climent, Michael Neumann   +2 more
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A Block Projection Method for Sparse Matrices

SIAM Journal on Scientific and Statistical Computing, 1992
For the solution of systems of linear algebraic equations with sparse matrices the block Cimmino method is employed. Let the system be written as \[ \begin{pmatrix} A^ 1\\A^ 2\\\vdots\\ A^ p\end{pmatrix} x=\begin{pmatrix} b^ 1\\ b^ 2\\ \vdots \\b^ p\end{pmatrix} \] where the \(A^ i\) are matrices and the \(b^ i\) vectors.
Mario Arioli, Iain S. Duff, Joseph Noailles, Daniel Ruiz 0002   +3 more
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A Note on Preconditioned Block Toeplitz Matrices

SIAM Journal on Scientific Computing, 1995
\textit{T. Ku} and \textit{C. Kuo} [ibid. 13, No. 4, 948-966 (1992; Zbl 0756.65048)] proposed and analysed a block circulant preconditioner \(R_{mn}\) for solving a family of block Toeplitz systems \(T_{mn} x = b\). In the present paper, it is proved that the matrix \(T_{mn}\) is positive definite if the generating function \(f(x,y)\) of \(T_{mn}\) is ...
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Hymniablock — Eigenvalue solver for blocked matrices

Computer Physics Communications, 1980
Reference CRPP-ARTICLE-1980-016doi:10.1016/0010-4655(80)90019-3View record in Web of Science Record created on 2008-04-16, modified on 2017-05 ...
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